ABSTRACT. Modern AI systems have achieved remarkable capabilities, yet they continue to struggle with reasoning, robustness under uncertainty, semantic controllability, and reliable generalisation across diverse tasks and environments. Addressing these challenges requires methods that meaningfully integrate data-driven learning with explicit representations of structure, knowledge, and inference. In this talk, I present a neuro-symbolic perspective on these challenges, grounded in work on learning from answer sets and extended to reward learning, task representations, foundation models, and controlled generation. I explore how symbolic representations and logical semantics can be learned from raw and noisy data, integrated with neural architectures, and used to support interpretable inference and reasoning across a range of settings. The research challenges I address include learning symbolic abstractions from perception, learning robust task representations for reinforcement learning, integrating symbolic reasoning with foundation models, and controlling the semantic behaviour of generative models. The central question unifying this work is how to build AI systems that are not only accurate, but semantically grounded, robust, and capable of reasoning that generalises well beyond the tasks they were trained on.

ABSTRACT. Insertion sequence variables have recently been introduced as a computational domain for modeling routing and sequencing problems in constraint programming. Typically, search heuristics guide the insertion process of new nodes into a partial growing path, while constraints eliminate infeasible insertions. This paper investigates filtering for the (minimum) distance constraint over insertion sequence variables. This global constraint links a sequence to a distance variable based on a given distance matrix. So far, only a simple filtering algorithm has been proposed, which considers the partial path but ignores mandatory nodes. Our contribution is to introduce stronger lower bounds that also take mandatory nodes into account. These bounds further enable the derivation of additional filtering rules for node insertions. An experimental evaluation on the TourMustSee problem shows that the proposed filtering rules significantly reduce the search space compared to the existing filtering approach.

ABSTRACT. We study the p-dispersion problem with distance constraints (pDD). In a pDD, the goal is to locate a set of facilities maximizing the minimum distance between any two of them, subject to constraints specifying minimum allowed distances. Two CP models for the pDD have been proposed. The first includes the global constraints Minimum and Element (or Table) and explicitly represents the objective function, connecting it to the decision variables, whereas the second only uses binary constraints. Here, after demonstrating the deficiencies of these models, we propose a new one that captures pDDs  through ternary constraints. We prove that the pruning of the decision variables achieved in our new model is equivalent to that achieved in the global constraints model, giving the same search tree under the same variable and value ordering. Experiments demonstrate that our new model is greatly superior to existing ones in both solution quality and run times.

ABSTRACT. The Bound-Impact Value Selector (BIVS) employs a look-ahead strategy to enable black-box Constraint Optimization Problem (COP) solvers to find high-quality solutions earlier. However, its computational cost prohibits its use throughout the entire search process. To mitigate this cost, the Restricted Fixpoint (RF) approach considers only the constraints on the shortest paths between the selected variable and the objective, yielding better performance. In this paper, we propose a lightweight strategy from a different perspective, named Assess Before Look-Ahead (ABLA), to enhance the performance of look-ahead-based value heuristics for solving COPs. ABLA first assesses whether the look-ahead process can differentiate between the values of a variable, and only performs the look-ahead when this assessment passes. Experiments on benchmark instances from recent MiniZinc Challenges demonstrate that ABLA’s decisions to skip redundant look-ahead processes are highly reliable, with an average accuracy of over 94%. Consequently, ABLA significantly boosts the performance of both BIVS and RF, outperforming two other baselines: the minimum value heuristic and the RLARF value heuristic.

ABSTRACT. In the context of optimally solving classical planning problems using constraint programming (CP), recent work has shown the potential of concisely factorizing tasks into deterministic finite automata. Finding a plan that solves the task is therefore reduced to finding a word accepted by all automata, through Regular constraints. So far, these automata had to be carefully handcrafted from PDDL tasks. In this paper, we show that such automata can be automatically generated and used as a base to form CP models. We also show that this framework is easily extensible with additional constraints, such as landmark constraints from the planning literature, to strengthen the models. We compare our approach to the state-of-the-art in CP for classical planning and observe that our framework is competitive with these baselines, and even outperforms them in several domains.

ABSTRACT. Logistics optimization frequently involves complex routing decisions bound by tight numerical constraints like vehicle capacities. This paper addresses a real-world industrial multi-batching problem where products are routed between distributed sites to determine optimal routes, travel frequencies, and packing configurations at minimum cost. This couples a minimum cost flow problem with a bin packing problem. We investigate direct formalizations, advanced decompositions, and scalable heuristic sequential approaches across three base technologies: Mixed-Integer Linear Programming, Constraint Programming, and Answer Set Programming. Our contributions are threefold: we propose a direct formalization of the problem, additional distinct approaches that scale for an industrial use case, and finally an empirical evaluation. By comparing these approaches we highlight the most effective configurations. Finally, it seems that combining MILP for flow routing with CP for packing decisions offers the best solution for scaling to the industrial logistics use case.

ABSTRACT. We study a routing problem for delivering and picking up multiple commodities with different priorities, motivated by the need to provide basic services to people in depopulated rural areas with a driver shortage. We define our problem as a generalization of the team orienteering problem with time windows, with additional constraints motivated by real-world applications. We develop constraint programming (CP) and mixed-integer programming (MIP) models to solve the formulated problem. In addition, we propose an incremental warm-starting strategy, which obtains an initial solution by solving a problem considering only a subset of commodities. In our experiment, CP outperforms MIP, and incremental warm-starting improves the performance of both approaches.

ABSTRACT. Heating, Ventilation, and Air Conditioning (HVAC) systems typically aim to regulate a building's indoor environment, considering occupant comfort, air quality, material cost and energy efficiency. Many key design decisions which carry strong consequences on HVAC systems, are made during early-stage building design, when architectural and structural layouts are still evolving. Early coordination between disciplines has the potential to minimise re-design of systems as a consequence of changes in other systems. This paper presents an optimization-based framework to support early design coordination among architectural, structural and mechanical designs, with a focus on ductwork layout. We develop models for generating feasible duct layouts directly from floor plans while accounting for structural constraints and cost objectives. The models are implemented in a high level modelling language MiniZinc and solved in phases using Constraint Programming (CP) and Mixed-Integer Programming (MIP) solvers. Experiments on real-world case studies show that feasible coordinated layouts can be generated, enabling iterative exploration of multiple alternatives during early-stage design.

ABSTRACT. In professional sports, a team has clinched the playoffs if they are guaranteed a postseason spot, regardless of the outcomes of any remaining games. As the season progresses, sports fans are interested in precisely when, and under what conditions, their team will clinch the playoffs. In this paper, we investigate playoff clinching in the context of the National Hockey League (NHL), where it is computationally-challenging to produce clinching scenarios due, in part, to complex tie-breaking rules. We present an algorithm that determines under which combinations of game outcomes in the next n days a team will clinch the playoffs (i.e., ``n-day look-ahead clinching''). Our approach is a custom tree search which employs various pruning and pre-processing techniques and ordering strategies, to efficiently explore the space of possible outcomes. The tree search leverages a constraint programming (CP)-based subroutine for inference that determines if a team has clinched the playoffs for some snapshot in time of the regular season (i.e., ``0-day look-ahead clinching''). This CP subroutine aims to find a counter-example in which the team being evaluated is eliminated, taking into account qualification rules and the NHL's extensive list of tie-breaking procedures. We validate the efficacy of our algorithm using hundreds of scenarios based on public NHL data for the seasons 2021-22 through 2024-25. The methods introduced can be readily extended to other metrics of interest, including mathematical proof of playoff elimination, clinching the President's Trophy, as well as clinching (or being eliminated from clinching) any other seed in the standings.

ABSTRACT. Cancer is often driven by specific combinations of an estimated two to nine gene mutations, known as multi-hit combinations. Identifying these combinations is critical for understanding carcinogenesis and designing targeted therapies. We formalise this challenge as the Multi-Hit Cancer Driver Set Cover Problem (MHCDSCP), a binary classification problem that selects gene combinations to maximise coverage of tumor samples while minimising coverage of normal samples. Existing approaches typically rely on exhaustive search and supercomputing infrastructure. In this paper, we present constraint programming and mixed integer programming formulations of the MHCDSCP. Evaluated on real-world cancer genomics data, our methods achieve performance comparable to state-of-the-art methods while running on a single commodity CPU in under a minute. Furthermore, we introduce a column generation heuristic capable of solving small instances to optimality. These results suggest that solving the MHCDSCP is less computationally intensive than previously believed, thereby opening research directions for exploring modelling assumptions.

ABSTRACT. We study integer programming (IP) encodings of acyclicity in directed graphs as a key constraint in various real-world problem domains. We analyze both classical and more recently-proposed acyclicity encodings, including Miller--Tucker--Zemlin (MTZ), feedback vertex set (FVS), vertex elimination (VE), and cycle elimination (CE) based encodings in terms of their linear programming (LP) relaxation tightness. We also introduce hybrid encodings combining sought-after properties of the individual encodings. For the hybrids, we establish tightness guarantees for their LP relaxations that interpolate smoothly between the individual encodings. Our results show that VE and CE yield equally strong relaxations and strictly dominate MTZ and FVS, while the hybrid encoding schemes become increasingly tight as the elimination prefix grows. Mapping theory to practice, we empirically evaluate the encodings on both direct IP encodings of problem domains, where acyclicity is a key constraint, as well as on IP translations of answer set optimization (ASP) models. The results both validate our theoretical findings and yield promising runtime performance.

ABSTRACT. Many edge-selection problems, such as the Traveling Salesman Problem and Orienteering Problem, are NP-hard, making them expensive to solve with exact methods and challenging to address with hand-crafted heuristics. Learning-based approaches provide an efficient alternative, while self-supervised methods avoid costly solution labels. However, existing approaches often still rely on heavy post-processing or narrow problem-specific designs. We propose a reusable self-supervised framework for edge-selection optimization that learns directly from unlabeled instances. The framework uses differentiable surrogate objectives and feasibility-driven penalties to encourage the model to learn feasibility-aware solution structure during training. To support efficient inference, we introduce a lightweight graph architecture centered on a cost-attention convolution, where edge costs and feasibility information directly shape message passing. Experiments on three problem families demonstrate strong solution quality and efficient inference across diverse edge-selection settings.

ABSTRACT. Many real-life problems involve multiple conflicting objectives. In such settings, a single solution rarely optimizes all objectives; hence, the decision maker is provided with a set of trade-off solutions, the Pareto front. While many methods to compute Pareto fronts have been proposed in the operations research community, comparatively few approaches are available for constraint programming (CP). One of the main state-of-the-art algorithms in CP is a branch-and-bound method combined with a Pareto global constraint, denoted here as MOBAB-CP. In this work, we implement SAUGMECON, an $\epsilon$-constraint method, in a CP solver, using a global constraint to perform lexicographic optimization instead of the augmented objective function used in SAUGMECON. We also propose a SAUGMECON-inspired algorithm that integrates the Pareto global constraint. Experimental results show that the proposed algorithm consistently achieves better results than our CP implementation of SAUGMECON and is competitive with MOBAB-CP, outperforming it on several of the studied problems.

ABSTRACT. In the wood industry, ensuring the stability and immobility of a workpiece during machining is essential. Vacuum suction cups are commonly used as fixtures, as they can rotate to better conform to the workpiece perimeter. However, this rotational capability introduces additional complexity into fixture placement. This paper addresses the problem of optimally positioning rotatable fixtures by combining two complementary techniques. First, we solve a restricted version of the problem that neglects rotations using a constraint solver, yielding an initial feasible solution. This solution is then refined using a Particle Swarm Optimization algorithm that accounts for rotation. Experimental results show that the quality of initial solution significantly influences the final placement, and that the proposed approach can effectively support expert operators in making improved placement decisions.

ABSTRACT. Recent advances in AI have spurred interest in NeSy architectures that integrate neural and symbolic methods. In particular, combining a Constraint Programming (CP) model with a language model for constrained sequence generation tasks allows the neural component to capture domain knowledge while CP enforces structural constraints. In this paper we propose combining CP with a Masked Language Model (MLM) to perform Large Neighbourhood Search (LNS). Unlike conventional left-to-right Large Language Models, MLMs can complete sequences with gaps in arbitrary positions, making them well-suited for this task. For its part LNS provides a CP-based iterative framework to explore constrained subspaces whenever searching the whole space would be intractable. Experiments on constrained text generation and molecule discovery tasks demonstrate that NeSyLNS can quickly generate many high-quality sentences and molecules even for highly constrained tasks.

ABSTRACT. Inspired by concepts of constraint-based local search, we present a novel scheme for automatically relaxing a given high-level model into an optimisation model that is better suited for large neighbourhood search (LNS). By exploiting the variable sharing and semantics of the constraints in a model, our scheme (1) identifies constraints that can easily be satisfied simultaneously and can thus constrain the neighbourhood, and (2) relaxes the remaining constraints. As a side effect, our scheme enables the LNS solving of a constraint satisfaction problem, by transforming it into an optimisation problem, and the faster solving of a difficult-to-satisfy constrained optimisation problem, by finding the initial incumbent faster. This approach can be used with any CP-based LNS solver. We tested a portfolio of CP-based LNS solvers in parallel, and a multi-armed bandit to select which solver to run. Initial results show that on many problems our approach pays off.

ABSTRACT. Algorithms for solving combinatorial optimisation problems often exhibit complementary strengths, motivating automated algorithm selection by training ML models that predict the best algorithm for a given instance. However, training such models is computationally expensive, as it requires running every algorithm in a portfolio on all training instances. Recent work on frugal algorithm selection shows that training data can be reduced substantially through active learning, but the interaction between model choice and data efficiency remains poorly understood. In this work, we empirically investigate how different learning formulations behave under limited training budgets using the ASLib benchmark. Our results reveal that multiclass (MC) classification, despite being a weak passive learner, improves dramatically with active learning. Remarkably, active MC matches strong passive learners while using only a fraction of the training data. This highlights an unexpected efficiency gain: simple models uncompetitive under passive learning become highly effective when training data is selected actively.